Original article Tree mechanics and wood mechanics: relating hygrothermal recovery of green wood to the maturation process J Gril, B Thibaut Laboratoire de Mécanique et Génie Civil (URA 1214 du CNRS), Université de Montpellier II, place Eugène-Bataillon, CP 081, 34095 Montpellier Cedex 5, France (Received 24 December 1992; accepted 13 July 1993) Summary — Growth stress can be approached from the point of view of the mechanical standing of trees as well as that of the loading history applied to the material before tree felling. Stress origi- nates in wood maturation causing both rigidification and expansion to the cell-wall material. Locked- in strains are partially released by cutting specimens from the tree, and, more completely, by boiling them in a green state, so as to exceed to softening point of lignin. It has been supposed that the rheological conditions during such hygrothermal recovery might be similar to those existing during mat- uration, when lignification of the secondary cell wall occurred. A rheological model of wood in the pro- cess of formation is proposed to support this hypothesis and derive information on the average mat- uration rigidity. wood rheology / viscoelasticity / growth stress / hygrothermal recovery / cell wall Résumé — Mécanique de l’arbre et mécanique du bois. Relation entre la recouvrance hygro- thermique du bois vert et le processus de maturation. Les contraintes de croissance peuvent être abordées du double point de vue de la tenue mécanique des arbres et de l’histoire du chargement appli- qué sur le matériau jusqu’à l’abattage de l’arbre. Elles trouvent leur origine dans la maturation du bois qui provoque à la fois la rigidification et l’expansion de la matière constitutive des parois. Les déformations bloquées sont partiellement relâchées lorsque des échantillons sont extraits de l’arbre ; elles le sont plus complètement si ceux-ci sont chauffés à l’état vert au-dessus de la température de transition de la lignine. On a émis l’hypothèse d’une similarité des conditions rhéologiques de cette recouvrance hygrothermique avec celles qui prévalent lors de la maturation, caractérisée par la lignification de la paroi secondaire des cellules. Une analogie rhéologique représentant le comportement du bois au cours de sa forma- tion a été proposée dans le but d’appuyer cette hypothèse et d’en déduire des informations sur la rigidité moyenne de maturation. rhéologie du bois / viscoélasticité / contrainte de croissance / recouvrance hygrothermique / paroi cellulaire INTRODUCTION In the review by Kübler (1987) on growth stresses, a whole chapter dealt with the thermal strain of green wood, characterised by a tangential swelling and a radial shrink- age. Since Koehler (1933) and MacLean (1952) these have been identified as the main cause of heart checking during log heating (fig 1) (Gril et al, 1993b). This abnor- mal thermal strain results from the visco- elastic recovery of growth stress (Kübler, 1959c) and for that reason it is called ’hygrothermal recovery’ (HTR) after Yokota and Tarkow (1962). These authors clarified the contribution of conventional thermal expansion, cell-wall drying due to the decrease of fiber saturation point, and visco- elasticity, to the total thermal strain. Kübler (1973a, 1973b) went one step further in the fundamental understanding of HTR when he observed that the viscoelastic contribu- tion is not the mere amplification of instan- taneous release strains observed during tree felling and subsequent processing oper- ations. The greater part of ’true’ HTR must be related to the maturation process, ie the last stage of secondary cell formation char- acterised by polymerisation of lignin monomers and completion of cellulose crys- tallisation in the cell wall. The remaining part results from the action of subsequently formed wood layer. In the past years, research on growth stress has received growing interest from French teams (Guéneau, 1973; Saurat and Guéneau, 1976; Chardin and Bege, 1982). It has recently evolved into a more comprehen- sive approach where the regulation of tree form is studied in relationship to tree archi- tecture, wood structure and tree mechan- ics (Thibaut, 1989, 1990, 1991, 1992; Loup et al, 1991; Fournier et al, 1992). The main objective of this paper is to show that HTR studies might contribute to this general framework of research because they involve simultaneous investigations on the material properties (wood rheology), the mechanics of the living structure (tree mechanics), and the transformation of a living structure into material (wood processing). Tree mechanics and wood mechanics Two points of view are made implicit in the research on architecture, structure and mechanics of trees. Trees appear as com- plex structures managing to stand up through the wood constituting their stem. On the other hand, wood is considered as a material that has been produced by trees and thus has gained properties depending on the biological conditions of its elabora- tion. Figure 2 shows that a different use of the temporal dimension underlies these 2 points of view. The discs correspond to the cross-section of a portion of stem axis; this is a level of observation that is most ade- quate to link the 2 fields of research. Only smooth variations of wood properties are observed at this level, such as juvenile/adult wood or sapwood/heartwood transitions. Local variations like intra-ring heterogene- ity, corresponding to seasonal cycles, are not accounted for. For the tree stem, time started when the pith was initially placed in the space explored by the bud. As the stem grows older, it increases in diameter. For wood, time started when it was made; the nearer to the pith, the older the wood. Two opposite directions of time result, as shown by the arrows: stem age increases towards the periphery; wood age increases towards the centre. The juvenile/adult wood transition (fig 2, top left) is related to the age of the stem, while the sapwood/heart- wood transition (fig 2, top right) is related to the age of the wood. We do not mean to suggest that a direct causal relationship exists between stem age and the transi- tion form juvenile to adult wood, or between wood age and heartwood formation, although it might be partially the case, we simply have in mind here the location of events in time. This results in a 2-fold approach to growth stress in trees, illustrated at the bot- tom of figure 2 by different representations of the history of the longitudinal growth stress. From the tree mechanics standpoint (fig 2, bottom left), we deal with successive stages of stem development, where the existence of a self-equilibrated stress field participates in the overall mechanical stand- ing of the tree. From the wood mechanics standpoint (fig 2, bottom right), we are con- cerned with the loading history to which the material has been subjected since the moment of its creation until the tree was felled and wood started to exist as a ’tech- nical’ material. What happened to wood while it was a part of the tree, ’in tree’ wood, could be called the ’prehistory’ of the wood, as opposed to the history of ’outside-tree’ wood. The ’history’ of the material includes cutting, drying and various treatments. Such data are more or less accessible provided that records of what happened to the wood since the tree was felled have been kept. Its ’prehistory’, however, is not directly accessible. In order to estimate prehistoric factors, we have to question trees, like his- torians who must rely on mythic or folklore records and a few archaeological remains, to figure out what humanity was and did in ancient times (Gril, 1991a). Stress profiles and corresponding stress histories, such as those shown in figure 2, can be calculated theoretically, based on assumptions about stem growth and geom- etry, constitutive equations of wood, and the mechanical effect of maturation. For instance, Kübler (1959a, 1959b) consid- ered the case of a long cylindrical stem por- tion with circular cross-section, made of an elastic, homogeneous and transversally isotropic material, subjected at the peri- phery to an initial growth stress having non- zero components in the longitudinal and tangential directions only. Later more com- plex situations were considered (Archer, 1986). Although more realistic stress pro- files can be obtained, in particular near the centre, by accounting for the different prop- erties of juvenile wood (Fournier, 1989), all these calculations assumed elastic behaviour. Sasaki and Okuyama (1983) have shown the limits of the elastic approach by actually measuring radial vari- ations of both the stress field and the elas- tic constants. They found a systematic gap between prediction and reality whatever additional assumptions they made. At the same time, they measured hygrothermal recovery of wood specimens taken from corresponding portions of the same trunk, and observed that the gap could be related to the amount of viscoelastic locked-in strain liberated by the heating test. Such results suggest that a viscoelastic approach of growth-stress generation might improve the prediction of stress profiles (fig 3) and, consequently, yield a more realistic analysis of the stress histories applied to the material, depending on its radial posi- tion at the time of tree felling (fig 4). THE MECHANICAL CONSEQUENCES OF MATURATION Growth stress originates in the maturation process. Wood maturation includes all the biochemical processes happening after the deposition of secondary layers, such as lignin polymerisation, completion of cellu- lose crystallisation, or cross-linking in the amorphous regions of the cell-wall mate- rial. For most of the cells (parenchyma cells must be excepted), this process corre- sponds to the end of the biological activity, but it is also the most active period mechan- ically, because the expansion tendency characterising cell maturation occurs after a certain amount of rigidity has been acquired by the cell wall. The main definitions used to described the successive stages of wood formation and transformation are illustrated schematically in terms of stress and strain in figure 5. The amount of deformation that a given portion of newly formed wood (fig 5a) tends to reach will be defined as the matu- ration strain (fig 5b). As most of this defor- mation is prevented by the neighbouring layers, especially in the tangential and longi- tudinal directions, the new portion of wood is put under stress, named here the initial growth stress (fig 5c). The method used to evaluate the initial growth stress consists of isolating a portion of wood located near periphery and measuring the instantaneous recovery (fig 5d). If the piece of wood is left for some time, there will be a delayed recov- ery, that might be considerably accelerated by heating while still wet, which provokes hygrothermal recovery (fig 5e). The separation between an instanta- neous and a delayed component of recovery might seem arbitrary. Indeed, some stress relaxation may occur between the various steps of experimental measurements. For the sake of simplicity, we assume that the amount of delayed recovery at ambient tem- perature remains negligible compared with that obtained through hygrothermal treat- ment. Moreover, we have purposely drawn identical wood portions in figures 5b and 5e, to suggest a rheological similarity between maturation and hygrothermal recovery, which will be discussed later. Although cell-wall formation, especially maturation, is very short (a few weeks) com- pared with the subsequent duration of wood existence as a supporting part of the stem, it is of the utmost importance both for the tree stem and for the wood, because of its mechanically active mature (Wilson and Archer, 1979; Fournier et al. 1992). Angular variations of initial growth stress provide the stems with the only mechanism of secondary reorientation compatible with their thickness and rigidity. The amount of maturation strain and the resulting initial growth stress depend on morphological fac- tors (such as the mean inclination of cellu- lose crystallites in the secondary walls, or the lignin content), which can be adjusted during the formation of the secondary wall under the action of growth regulators. The formation of reaction wood is an extreme illustration of the potential for such morpho- logical variations. Wood layers located near the stem periphery are pre-strained by longitudinal tension and tangential compression as the expense of less vital internal layers, sub- jected by compensation to longitudinal com- pression and transverse tension. This situ- ation favours stem flexibility and tends to prevent breaking or surface damage under bending loads, as illustrated in figure 6. This shows the effect of stem bending on the variation of peripheral strains relative to an assumed failure criterion in strain space; bending strains may reach more consider- able levels, when superimposed on periph- eral prestrains, without provoking either lon- gitudinal or transverse rupture. Biochemical reactions occurring during maturation tend to increase the molecular mobility of the cell-wall material dramati- cally, so that the viscoplastic effect of stresses is considerably higher than in mature wood. We deal here with a ’chemo- rheological’ situation, similar in some way to the so-called ’mechano-sorptive’ effect observed during loading under moisture changes (Grossman, 1976; Gril, 1991a), only more pronounced. A MODEL OF MATURATION AND RECOVERY Maturation determines the essential fea- tures of the material. It would thus be a great achievement to gain knowledge on the tran- sient mechanical properties of wood during the process of formation. There is no direct way of obtaining such information, basically because wood responds actively to stresses during its formation, and in such situations conventional approaches of solid rheology lose their validity. To obtain some informa- tion, we have proposed an indirect approach which has been detailed elsewhere (Gril, 1991 b), the principles of which are sum- marised here. What matters in the maturation process, from the mechanical point of view, is the existence of a gradual rigidification followed by a gradual expansion tendency (matura- tion strain). As shown in figure 7a, both pro- cesses may be partially simultaneous, but there has to be a time gap so that the mate- rial starts to expand after having gained some rigidity. For the purpose of modelling, in figure 7b we propose replacing in the sim- plest possible way, the gradual changes by step changes with an equivalent qualitative effect. During the period called ’maturation’ (between t1 and t3 ), the material has a rigid- ity intermediate between ’zero’ represent- ing the very low rigidity at the end of pri- mary wall formation, and ’mature’ corresponding to the final state of biologi- cally dead and mechanically passive wood. At some time t 2 during maturation, the mat- uration strain appears. The rheological analogy illustrated in fig- ure 8 accounts for the 2-fold nature of the maturation process. It is made of a series of 3 rheological elements: (i) an elastic mech- anism represented by a spring of rigidity K (equal to that of mature wood), strained by σ/K under the external stress σ. (ii) A vis- coelastic mechanism represented by a spring of rigidity K’ and a dashpot having a characteristic time τ which is very small dur- ing the maturation process (τ << t3- t1 ), but much larger afterwards. In other words, dur- ing maturation the dashpot is ’open’ and the element acts like an elastic spring K’ strained by β = σ/K’, in the mature state, the dashpot ’locks’ the mechanism and allows only slow viscoelastic variation of β. (iii) A maturation strain changing suddenly from 0 to μ at time t2. A newly deposited wood portion might be represented at time t < t 2 (before matu- ration strain) by such a rheological analogy, with unstrained springs and zero stress. At time t2, due to the expansion μ and the par- tial obstacle from neighbouring parts, which restricts the deformation, the wood sub- jected to the initial growth stress σ i. It responds as if it had no dashpot, so that the total strain is equal to: where ϵ i is the initial growth strain actually allowed by the surrounding structure. At time t3 nothing changes in the respective extension of the elements: the stress remains σ = σ i , and the viscous compo- nent of strain β = β i = = σ i /K’. Later (at times t> t3 ), under the influence of stem growth, σ and β will be slowly modified according to some rate law, such as, for instance, a first- order rate law: If the wood portion represented by our model has been recently formed, it is still subjected to a stress approximately equal to the initial growth stress σ i . Now let us imagine that it is suddenly isolated from the surrounding material. The stress σ to which it is subjected falls from σ i to zero, resulting in a stress increment Δσ=-σ i and a strain increment: where α corresponds to the instantaneous peripheral released strain measured experi- mentally on standing trees (Archer, 1986; Chanson et al, 1992). RELATING HTR TO THE MATURATION PROCESS After the recently formed wood portion has been extracted, the material remains strained, relative to the original dimensions prior to maturation by ϵ i + α = μ + σ i / K’. The maturation strain μ cannot be released in any way, because it was caused by irre- versible modifications of the cell-wall mate- rial. The second component (σ i /K’), how- ever, is of a viscous nature, so that in theory it can be recovered provided the conditions for viscoelastic recovery are fulfilled. These are either time or temperature (Grzeczyn- sky, 1962; Kübler, 1987). On the other hand, the main difference between wood in the process of maturation and mature material is the lignification of the cell wall. As lignin has been shown to play a major role in the stimulation of hygrothermal recovery (Kübler, 1987; Gril et al, 1993a), to assume a rheo- logical similarity between the 2 situations holds some physical basis. Although it remains to be proven and quantified, based on such physical considerations, we pro- pose here the following working hypothe- sis (fig 9): A hygrothermal treatment induces visco- elastic conditions similar to those that existed during maturation. Consequently, if a piece of wood previ- ously separated from the tree (after mea- surement of α) is sufficiently heated in water, it undergoes a hydrothermal recovery: One should be aware of the fact that although the strain recoveries (α and η) and the elastic rigidity of mature wood (K) are measurable quantities, the term K’ does not bear such a clear mechanical meaning and cannot be observed directly. It corresponds to an ’average’ mechanical response of wood in the process of maturation, not at any given instant. From the combination of equations [3] and [4], we deduce that α and η are related to each other by a simple equation: suggesting that a combination of data on α, η and Kcould provide indirect information on the components of K’. Although figure 8 makes use of linear elements such as a spring, a dashpot, etc, to represent the mechanical behaviour of the material, all the preceding quantities must be consid- ered as multiaxial tensors. Strain variables like ϵ, α and η or stresses like σ and σ i are described at least by 6 components, corresponding to the 3 extensions and the 3 shears in perpendicular directions R (radial), T (tangential) and L (longitudinal). Rigidi- ties like Kor K’ must relate 6 components of stress to 6 components of strain. In Gril (1991b), we have derived multiaxial equa- tions and obtained estimates of K’ compo- nents according to some additional hypo- thesis made on its mathematical form. CONCLUSION Hygrothermal recovery data provide us with information complementing that provided by instantaneous recovery measurements. In the case of the peripheral material exam- ined here, the analysis has been made sim- pler because the locked-in strain has not yet been modified by loading changes pro- voked by subsequent stem growth. The observed recovery can thus be directly related to the rheological conditions of mat- uration. 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Original article Tree mechanics and wood mechanics: relating hygrothermal recovery of green wood to the maturation process J Gril, B Thibaut Laboratoire de Mécanique et Génie. tree’ wood, could be called the ’prehistory’ of the wood, as opposed to the history of ’outside-tree’ wood. The ’history’ of the material includes cutting, drying and various. the periphery; wood age increases towards the centre. The juvenile/adult wood transition (fig 2, top left) is related to the age of the stem, while the sapwood/heart- wood